This invention is related to a digital distance relay for measuring impedance up to the point of the fault with a fault point resistance in an AC power supply system with load current.
Impedance of the distance relay in the prior art is set by estimating impedance measurement errors arising from fault with resistance of fault point in a power supply system with load current. At a sending terminal, tendency of so called xe2x80x9cover-reachxe2x80x9d is seen where reactance component of the impedance is seen smaller than actual value. At a receiving terminal, tendency of so called xe2x80x9cunder-reachxe2x80x9d is seen where reactance component of the impedance is seen larger than actual value.
However, terminals where a distance relay is set are not fixed to the sending side or the receiving side, and impedance is usually set considering maximum of the error that can be generated under estimated system conditions.
FIG. 1 shows a digital distance relay 10 set in a power supply system. As shown in FIG. 1, the digital distance relay 10 receives total current xe2x80x9cI+ILxe2x80x9d of load current IL and fault current xe2x80x9cIxe2x80x9d from a transmission line 1 via a current transformer 2, and voltage V transformed to an appropriate level via a voltage transformer 3. The voltage V consists of a voltage drop component xe2x80x9cR+jXxe2x80x9d due to the impedance of the transmission line and fault point voltage VF due to fault current I/C (wherein C is a current division ratio of the fault current) through the fault point resistance RA at the fault point F, as shown in Equation (1) below:
V=Rxc2x7(I+IL)+jXxc2x7(I+IL)+VFxe2x80x83xe2x80x83(1)
where VF=RAxc2x7I/C, and xe2x80x9cjxe2x80x9d is an imaginary unit of complex numbers. In Equation (1), the fault point voltage VF is a cause of error in impedance measurement of distance relays.
Equation (1) can be transformed to Equation (2) shown below:                                                                         V                /                                  (                                      I                    +                    IL                                    )                                            =              Zry                                                                          =                              R                +                jX                +                                                                            (                                              RA                        /                        C                                            )                                        /                                          (                                              1                        +                                                  IL                          /                          I                                                                    )                                                        _                                                                                        (        2        )            
because:                     ZF        =                                            (                              RA                /                C                            )                        /                          (                              1                +                                  IL                  /                  I                                            )                                _                                        =                  rf          +          jxf                    
The impedance of the underlined part of Equation (2) results in impedance measurement error as shown in FIG. 2.
In FIG. 2, FB corresponds to RA/C in Equation (2), and FA corresponds to the fault impedance seen from the relay corresponding to the underlined part of Equation (2).
The ratio of the magnitudes of FA and AB is |IL/I|, and the phase difference xcex4 between FA and FB shows advanced phase of the load current relative to the fault current I. When the magnitude |IL/I| is changed with a constant phase difference xcex4, the trace of the impedance Zry seen from the relay becomes a circle as shown in FIG. 2. This circle is a trace of the point A where the circumference angle ∠FAB viewing a chord FB (=RA/C) is a constant of ∠FAB=xcfx80xe2x88x92xcex4.
The resistance component rf and the reactance component xf of the measurement error of the impedance seen from the relay are calculated as follows:
Equation (1) is multiplied by (I+IL)*, which is a conjugate complex number of the current (I+IL) which is applied when the impedance is measured with the relay, and then the real and imaginary parts of both side are respectively equalized as shown in Equations (3) and (4) as follows:
Re[Vxc2x7(I+IL)*]=Rxc2x7|I+IL|2+Re[VFxc2x7(I+IL)*]
Re[Zry]=R+Re[VFxc2x7(I+IL)*]/|I+IL|2 xe2x80x83xe2x80x83(3)
Im[Vxc2x7(I+IL)*]=Xxc2x7|I+IL|2 +Im[VFxc2x7(I+IL)*]
Im[Zry]=X+Im[VFxc2x7(I+IL)*]/|I+IL|2 xe2x80x83xe2x80x83(4)
The underlined parts of Equations (3) and (4) are the impedance measurement error xe2x80x9crf+jxfxe2x80x9d.
Mathematically in general, Vectors A and B have the following relations:
[Axc2x7B*]=|A|xc2x7|B|xc2x7exp(j(xcex8))
Im[Axc2x7B*]=|A|xc2x7|B|xc2x7sin(xcex8)
Re[Axc2x7B*]=|A|xc2x7|B|xc2x7cos(xcex8)
wherein xe2x80x9c*xe2x80x9d denotes conjugate complex number, xcex8(=xcex8Axe2x88x92xcex8B) is an advanced phase of Vector A relative to Vector B. Considering the mathematics described above, Equations (3) and (4) show that, when the fault point voltage VF is delayed relative to the current xe2x80x9cI+ILxe2x80x9d which is used for impedance measurement of the relay, xf becomes negative, and the reactance Xry measured by the relay becomes smaller than the actual reactance X up to the fault point, which is an xe2x80x9cover-reachxe2x80x9d state. On the other hand, when the fault point voltage VF is advanced relative to the current xe2x80x9cI+ILxe2x80x9d, xf becomes positive, and the reactance measured by the relay becomes larger than the actual line reactance, which is an xe2x80x9cunder-reachxe2x80x9d state.
From the explanation above, it is understood that the measurement error of the digital distance relay for measuring the impedance up to the fault point changes much depending the direction and magnitude of the load current, in case of a fault with a load current and with a fault resistance. However, in the prior art, the digital distance relay is set considering maximum measurement error calculated based on the condition of the power supply system and the estimated magnitude of the fault point resistance.
Accordingly, it is an objective of the present invention to provide a digital distance relay preventing over-reach and under-reach by detecting phase difference between the current for measuring the impedance of the digital distance relay and the current which is in a substantially same phase as the fault point current. The performance of the distance relay is adjusted on real-time basis with the change of phase difference.
According to a first aspect of the present invention, there is provided a digital distance relay for deciding whether a fault point is within a stipulated operation region by obtaining an impedance up to the fault point through a line equation of a transmission line including terms of resistances and reactances using data of voltage and current of AC power supply system periodically sampled, the relay comprising: a first means for calculating positive-phase resistance Rcal and positive-phase reactance Xcal: a second means for storing load current a stipulated time period prior to the fault was detected: a third means for detecting current in same phase as fault current flowing through the fault point: a fourth means for detecting relative phase of the current detected by the third means relative to current for directly calculating the positive-phase resistance Rcal and the positive-phase reactance Xcal: a fifth means for deciding whether the impedance is within a specified region by applying a value proportional to the relative phase detected by the fourth means: and a sixth means for deciding the fault point is within the stipulated operation region if: (a) when the load current stored by the second means indicates a sending current direction, the positive-phase resistance Rcal and positive-phase reactance Xcal are within a stipulated region based on a stipulated positive-phase resistance and a stipulated positive-phase reactance, and the impedance is decided within the specified region by the fifth means; or (b) when the load current stored by the second means indicates a receiving current direction, the positive-phase resistance Rcal and positive-phase reactance Xcal are within a stipulated region based on a stipulated positive-phase resistance and a stipulated positive-phase reactance, or the impedance is decided within the specified region by the fifth means.
By the first aspect of the present invention, when an impedance of the transmission line from the relay point up to the fault point is measured and it is decided whether the fault point is within the stipulated operation range, even if the load current is flowing and the fault point has a fault point resistance and there is an impedance measuring error, the relay operates correctly by compensating the relay characteristics.
According to a second aspect of the present invention, there is provided a digital distance relay of the first aspect of the present, the third means comprising: means for detecting current during the fault which is subtracted by the load current stored in the second means, when the fault is a phase fault: and means for detecting zero-phase current, when the fault is a ground fault.
By the second aspect of the present invention, the current in substantially the same phase as the fault current flowing through the fault point is detected. The input current in the relay partly canceled by the load current is applied when there is a phase fault, and a zero-phase current is applied as a current corresponding to a fault current when there is a ground fault.
According to a third aspect of the present invention, there is provided a digital distance relay of the second aspect of the present invention, the third means comprising means for detecting electric values of xe2x80x9c(IVpc) /|Vp|xe2x88x92(ILVpc)M/|VpM|xe2x80x9d and xe2x80x9c(IVps)/|Vp|xe2x88x92(ILVps)M/|VpM|xe2x80x9d when the fault is a phase fault, where IVpc and IVps are, respectively, inner and outer products of the load current during the fault and a stipulated standard electric value, |VpM| is a magnitude of the stipulated standard electric value, (ILVpc)M and (ILVps)M are, respectively, inner and outer products of the load current stored in the second means and a stipulated standard electric value at a same time M, and |VpM| is a magnitude of the standard electric value at the same time M.
By the third aspect of the present invention, in case of a phase fault, the fault current is stored in two components, one in a same phase (i.e. inner product) and the other in a perpendicular phase (i.e. outer product) as the positive-phase voltage which does not change much through the occurrence of the fault, and in respect also of the current which is added by the load current during the fault, two components, one in a same phase and the other in a perpendicular phase as the positive-phase voltage are calculated. Then, the stored load current component prior to the fault is canceled from each component of the current during the fault, and the fault point current is detected in the same phase and in the perpendicular phase as the positive-phase voltage.
According to a fourth aspect of the present invention, there is provided a digital distance relay of the third aspect of the invention, the fourth means comprising:
means for calculating, in case of a phase fault,
Ipc={(Ips)/|Vp|xe2x88x92(ILVps)M/|VpM|}xc2x7(IVpc)/|Vp|xe2x88x92{(IVpc)/|Vp|xe2x88x92(ILVpc)M/|VpM|}xc2x7(IVPs)/|VP|xe2x80x83xe2x80x83(5)
and
Ips={(Ipc)/|Vp|xe2x88x92(ILVpc)M/|VpM|}xc2x7(IVpc)/|Vp|+{(IVps)/|Vp|xe2x88x92(ILVps)M/|VpM|56 xc2x7(IVps)/|Vp|xe2x80x83xe2x80x83(6)
from the IVpc and IVps which are, respectively, inner and outer products of the load current during the fault and a stipulated standard electric value, the electric values of xe2x80x9c(IVpc)/|Vp|xe2x88x92(ILVpc)M/|VpM|xe2x80x9d and xe2x80x9cIVps/|Vp|xe2x88x92(ILVps)M/|VpM|xe2x80x9d calculated by the third means, wherein xe2x80x9c(ILVpc)M/|VpM|xe2x80x9d and xe2x80x9c(ILVps)M/|VpM|xe2x80x9d are, respectively, components of the load current prior to the fault parallel and perpendicular to the standard voltage: and means for detecting relative phase of the current during the fault relative to the current in same phase as the current detected by the third means.
By the fourth aspect of the present invention, when a phase fault is detected, tan xcex8 is calculated where xcex8 is a phase angle between FA and FB shown in FIG. 2, through calculation of the inner and outer products of the current corresponding to the fault point current and the relay current by canceling the load current prior to the fault from the relay current for measuring impedance during the fault by the following equations:
The inner product of a current corresponding to the fault current and the current used when the impedance of the relay is measured (added by the load current):                                                         Ipc              =                              xe2x80x83                            ⁢                                                IF                  ·                  cos                                ⁢                                  xe2x80x83                                ⁢                θ                                                                                        =                              xe2x80x83                            ⁢                                                                    {                                                                                            (                          Ips                          )                                                /                                                  "LeftBracketingBar"                          Vp                          "RightBracketingBar"                                                                    -                                                                        (                          ILVps                          )                                                ⁢                                                  M                          /                                                      "LeftBracketingBar"                            VpM                            "RightBracketingBar"                                                                                                                }                                    ·                                                            (                      IVpc                      )                                        /                                          "LeftBracketingBar"                      Vp                      "RightBracketingBar"                                                                      -                                                                                                        xe2x80x83                            ⁢                                                {                                                                                    (                        IVpc                        )                                            /                                              "LeftBracketingBar"                        Vp                        "RightBracketingBar"                                                              -                                                                  (                        ILVpc                        )                                            ⁢                                              M                        /                                                  "LeftBracketingBar"                          VpM                          "RightBracketingBar"                                                                                                      }                                ·                                                      (                    IVps                    )                                    /                                      "LeftBracketingBar"                    Vp                    "RightBracketingBar"                                                                                                          (        7        )            
where xcex8=xcex8Fxe2x88x92xcex8i;
The outer product of a current corresponding to the fault current and the current used when the impedance of the relay is measured (added by the load current):                                                         Ipc              =                              xe2x80x83                            ⁢                                                IF                  ·                  sin                                ⁢                                  xe2x80x83                                ⁢                θ                                                                                        =                              xe2x80x83                            ⁢                                                                    {                                                                                            (                          Ipc                          )                                                /                                                  "LeftBracketingBar"                          Vp                          "RightBracketingBar"                                                                    -                                                                        (                          ILVpc                          )                                                ⁢                                                  M                          /                                                      "LeftBracketingBar"                            VpM                            "RightBracketingBar"                                                                                                                }                                    ·                                                            (                      IVpc                      )                                        /                                          "LeftBracketingBar"                      Vp                      "RightBracketingBar"                                                                      +                                                                                                        xe2x80x83                            ⁢                                                {                                                                                    (                        IVps                        )                                            /                                              "LeftBracketingBar"                        Vp                        "RightBracketingBar"                                                              -                                                                  (                        ILVps                        )                                            ⁢                                              M                        /                                                  "LeftBracketingBar"                          VpM                          "RightBracketingBar"                                                                                                      }                                ·                                                      (                    IVps                    )                                    /                                      "LeftBracketingBar"                    Vp                    "RightBracketingBar"                                                                                                          (        8        )            
and
tan xcex8=Ipc/Ips xe2x80x83xe2x80x83(9)
From those equations, advance or delay of the phase of the current during the fault to the current corresponding to the fault current flowing through the fault point.
According to a fifth aspect of the present invention, there is provided a digital distance relay of the first aspect of the present invention, the fourth means comprising: means for detecting relative phase of the current during the fault, in a case of a phase fault, relative to the current detected by the third means, based on a ratio of outer and inner products of a current xe2x80x9cIxe2x80x9d for directly calculating the resistance and the reactance, and a difference current xe2x80x9cxcex94Ixe2x80x9d between xe2x80x9cIxe2x80x9d and a current which is a stipulated period prior to the current xe2x80x9cIxe2x80x9d and which is in a same phase as the current xe2x80x9cIxe2x80x9d.
By the fifth aspect of the present invention, when a phase fault is detected, the inner and outer products of xcex94I and xe2x80x9cIxe2x80x9d are calculated and xe2x80x9ctan xcex8xe2x80x9d is calculated as follows, where xe2x80x9cIxe2x80x9d is a current for directly calculating resistance and reactance components, xcex94I=Ixe2x88x92IL (instant value) is a difference between xe2x80x9cIxe2x80x9d and IL which is the current at a time a stipulated period earlier (corresponding to a load current), and xcex8 is the phase angle between FA and FB shown in FIG. 2.
(xcex94Ixc2x7I)c=|xcex94Ixc2x7I|xc2x7cos(xcex8)
(xcex94Ixc2x7I)s=|xcex94Ixc2x7I|xc2x7sin(xcex8)
tan(xcex8)=(xcex94Ixc2x7I)s/(xcex94Ixc2x7I)cxe2x80x83xe2x80x83(10)
From the equations above, advance or delay of the phase of the current flowing during the fault to the current corresponding to the fault current flowing through the fault point is detected.
According to a sixth aspect of the present invention, there is provided a digital distance relay of the first aspect of the present invention, the fourth means comprising: means for detecting phase of current during the fault relative to the current detected by the third means when a ground fault has occurred, from a ratio of an outer product (I0xc2x7Ir)s and an inner product (I0xc2x7Ix)c; where the outer product (I0xc2x7Ir)s is an outer product of a zero-phase current I0 and a current Ir=ia+(krxe2x88x921)#i0, where xe2x80x9ciaxe2x80x9d is a ground fault phase current, xe2x80x9ckrxe2x80x9d is a value proportional to a ratio of a zero-phase resistance component and positive-phase resistance component of the transmission line impedance: and the inner product (I0xc2x7Ix)c is an inner product of a zero-phase current I0 and a current xe2x80x9cIx=ia+(kxxe2x88x921)xc2x7i0xe2x80x9d, where xe2x80x9ckxxe2x80x9d is a value proportional to a ratio of a zero-phase reactance component and positive-phase reactance component of the transmission line impedance.
By the sixth aspect of the present invention, when a ground fault is detected, a current Ir=ia+(krxe2x88x921)xc2x7i0 is applied to a current for calculating resistance and reactance components to calculate the outer product (I0xc2x7Ir)s and the inner product (I0xc2x7Ix)c. Then, tan(xcex8) is calculated as follows, where xcex8 is a phase angle between FA and FA shown in FIG. 2:
(I0xc2x7Ix)c=|I0xc2x7Ix|xc2x7cos(xcex8)
(I0xc2x7Ix)s=|I0xc2x7Ix|xc2x7sin(xcex8)
tan(xcex8)=(I0xc2x7Ir)s/(I0xc2x7Ix)cxe2x80x83xe2x80x83(11)
From the equations above, advance or delay of the phase of the current Ir and Ix for measuring resistance and reactance components up to the fault point during the fault to the zero-phase current xe2x80x9ci0xe2x80x9d corresponding to the fault current flowing the fault point is detected.
According to a seventh aspect of the present invention, there is provided a digital distance relay of the first aspect of the invention, the fifth means comprising: means for deciding, in case of a phase fault, that the relay should operate only if xe2x80x9ckxc2x7Ips/Ipcxe2x80x9d is larger than or equal to xe2x80x9c(Xcalxe2x88x92Xs)/(Rcalxe2x88x92Rs)xe2x80x9d, wherein Ips and Ipc are calculated by the fourth means, k is a pre-determined constant, Rcal is a resistance component calculated by the first means, Rs is a pre-determined resistance component, Xcal is a reactance component calculated by the first means, and Xs is a pre-determined reactance component.
By the seventh aspect of the present invention, when a phase fault is detected, the resistance component Rcal and the reactance component Xcal up to the fault point are separately calculated from the electric values between the short-circuited phases. Then, the relay is decided to operate when the following equation is satisfied, wherein the resistance component Rs and the reactance component Xs are pre-determined, and the electric values of Ips and Ipc are stipulated above:
Xcalxe2x88x92Xsxe2x89xa6(Ips/Ipc)xc2x7kxc2x7(Rcalxe2x88x92Rs)xe2x80x83xe2x80x83(12)
where k is a pre-determined constant.
The above equation is transformed as follows:
Ipcxc2x7(Xcalxe2x88x92Xs)xe2x89xa6kxc2x7Ipsxc2x7(Rcalxe2x88x92Rs)xe2x80x83xe2x80x83(13)
Where the constant k is put k=1.0+xcex5, and xcex5 is set positive when it is set larger than the calculated xcex8 shown in FIG. 3, and is set negative when it is set smaller, as shown in FIG. 3.
In FIG. 3, FA corresponds to the measured value of xcex8, and the line of xe2x80x9ck greater than 1xe2x80x9d corresponds to a tendency of xe2x80x9cunder-reachxe2x80x9d compared to the measured value, and the line of xe2x80x9ck less than 1xe2x80x9d corresponds to a tendency of xe2x80x9cover-reachxe2x80x9d compared to the measured value.
Thus, the impedance measurement error of the distance relay is compensated on real-time basis by calculating the current phase angle correlation based on the current corresponding to the fault point current and the current for the impedance measuring.
According to an eighth aspect of the present invention, there is provided a digital distance relay of the first aspect of the invention, the fifth means comprising: means for deciding, in a case of a ground fault, that the relay should operate only if (kxc2x7(I0xc2x7Ir)s/(I0xc2x7Ix)c) is larger than or equal to (Xcalxe2x88x92Xs)/(Rcalxe2x88x92Rs), wherein (I0xc2x7Ir)s and (I0xc2x7Ix)c) are calculated by the fourth means, k is pre-determined constant, Rcal is a resistance component calculated by the first means, Rs is a pre-determined resistance component, Xcal is a reactance component calculated by the first means, and Xs is a pre-determined reactance component.
By the eighth aspect of the present invention, when a ground fault is detected, the resistance component Rcal and the reactance component Xcal up to the fault point are separately calculated from the electric current compensated for zero-phase. Then, the relay is decided to operate when the following equation is satisfied, wherein the resistance component Rs and the reactance component Xs are pre-determined, and the electric values of (I0xc2x7Ix)c and (I0xc2x7Ir)s are stipulated above:
Xcalxe2x88x92Xsxe2x89xa6{(I0xc2x7Ir)s/(I0xc2x7Ix)c}xc2x7kxc2x7(Rcalxe2x88x92Rs)xe2x80x83xe2x80x83(14)
where k is a pre-determined constant.
The above equation is transformed as follows:
(I0xc2x7Ix)cxc2x7(Xcalxe2x88x92Xs)xe2x89xa6kxc2x7(I0xc2x7Ir)sxe2x88x92(Rcalxe2x88x92Rs)xe2x80x83xe2x80x83(15)
where the constant k is put k=1+xcex5, and xcex5 is set positive when it is set larger than the calculated xcex8 shown in FIG. 3, and is set negative when it is set smaller, as shown in FIG. 3.
Thus, the impedance measurement error of the distance relay is compensated on real-time basis by calculating the current phase angle correlation based on the current corresponding to the fault point current and the current for the impedance measuring.
According to a ninth aspect of the present invention, there is provided a digital distance relay of the seventh or eighth aspects of the invention, the sixth means comprising: means for deciding: when the load current stored by the second means is flowing in sending direction, that the relay should operate, if (Xcalxe2x88x92Xs)/(Rcalxe2x88x92Rs) is smaller than a pre-determined constant, and if the fifth means decides that the relay should operate: and when the load current stored by the second means is flowing in receiving direction, that the relay should operate, if (Xcalxe2x88x92Xs)/(Rcalxe2x88x92Rs) is smaller than a pre-determined constant, or if the fifth means decides that the relay should operate: wherein Rcal is a resistance component calculated by the first means, Rs is a pre-determined resistance component, Xcal is a reactance component calculated by the first means, and Xs is a pre-determined reactance component.
By the ninth aspect of the present invention, the operation characteristics is changed depending on the direction of the load current prior to the fault. Thus, the sixth means decides that: the region below the straight line NF and below the straight line FM shown in FIG. 4 is the relay operation region when the load current stored by the second means is in sending direction: while the region below the straight line NF or below the straight line FL shown in FIG. 5 is the relay operation region when the load current stored by the second means is in sending direction.
According to a tenth aspect of the present invention, there is provided a digital distance relay of the seventh or eighth aspects of the invention, the sixth means comprising: means for deciding: when Rcal is smaller than or equal to Rs, that the relay should operate, if (Xcal xe2x88x92Xs)/(Rcalxe2x88x92Rs) is smaller than a pre-determined constant, and if the fifth means decides that the relay should operate: wherein Rcal is a resistance component calculated by the first means, Rs is a pre-determined resistance component, Xcal is a reactance component calculated by the first means, and Xs is a pre-determined reactance component.